UPDATED: This will no longer unlock when obtaining 100 Dragon Teeth (checked on 184.108.40.206 on 2/19/16.
Dragon Teeth are earned from Raids and Special Dungeons, such as the Desert Dungeon and Dark Tower. The random boss raid, which is unlocked at Level 7, is likely the easiest (and quickest) way to generate Dragon Teeth, as it's possible to earn rewards of 2 and 4 Dragon Teeth depending on the level of the raid party. The Day 5 reward also gives 50 Dragon Teeth and Day 13 gives 100 Dragon Teeth, which can greatly help towards the count. In order to trigger the unlock conditions, however, a Tooth has to be earned from gameplay (not in-game reward) at 1000+.
1000 Dragon Teeth are required to meet the unlock.
100 Dragon Teeth are required to meet the unlock.